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Simplifying x2 + 24x + 62 = -9x + 6 Reorder the terms: 62 + 24x + x2 = -9x + 6 Reorder the terms: 62 + 24x + x2 = 6 + -9x Solving 62 + 24x + x2 = 6 + -9x Solving for variable 'x'. Reorder the terms: 62 + -6 + 24x + 9x + x2 = 6 + -9x + -6 + 9x Combine like terms: 62 + -6 = 56 56 + 24x + 9x + x2 = 6 + -9x + -6 + 9x Combine like terms: 24x + 9x = 33x 56 + 33x + x2 = 6 + -9x + -6 + 9x Reorder the terms: 56 + 33x + x2 = 6 + -6 + -9x + 9x Combine like terms: 6 + -6 = 0 56 + 33x + x2 = 0 + -9x + 9x 56 + 33x + x2 = -9x + 9x Combine like terms: -9x + 9x = 0 56 + 33x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-56' to each side of the equation. 56 + 33x + -56 + x2 = 0 + -56 Reorder the terms: 56 + -56 + 33x + x2 = 0 + -56 Combine like terms: 56 + -56 = 0 0 + 33x + x2 = 0 + -56 33x + x2 = 0 + -56 Combine like terms: 0 + -56 = -56 33x + x2 = -56 The x term is 33x. Take half its coefficient (16.5). Square it (272.25) and add it to both sides. Add '272.25' to each side of the equation. 33x + 272.25 + x2 = -56 + 272.25 Reorder the terms: 272.25 + 33x + x2 = -56 + 272.25 Combine like terms: -56 + 272.25 = 216.25 272.25 + 33x + x2 = 216.25 Factor a perfect square on the left side: (x + 16.5)(x + 16.5) = 216.25 Calculate the square root of the right side: 14.70544117 Break this problem into two subproblems by setting (x + 16.5) equal to 14.70544117 and -14.70544117.Subproblem 1
x + 16.5 = 14.70544117 Simplifying x + 16.5 = 14.70544117 Reorder the terms: 16.5 + x = 14.70544117 Solving 16.5 + x = 14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = 14.70544117 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = 14.70544117 + -16.5 x = 14.70544117 + -16.5 Combine like terms: 14.70544117 + -16.5 = -1.79455883 x = -1.79455883 Simplifying x = -1.79455883Subproblem 2
x + 16.5 = -14.70544117 Simplifying x + 16.5 = -14.70544117 Reorder the terms: 16.5 + x = -14.70544117 Solving 16.5 + x = -14.70544117 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-16.5' to each side of the equation. 16.5 + -16.5 + x = -14.70544117 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + x = -14.70544117 + -16.5 x = -14.70544117 + -16.5 Combine like terms: -14.70544117 + -16.5 = -31.20544117 x = -31.20544117 Simplifying x = -31.20544117Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.79455883, -31.20544117}
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